Answer:
9:2 36:8 72:12
Step-by-step explanation:
The functions f(x), g(x), and h(x) are defined:
f(x) = x
g(x) = 5x - 12
h(x) = x² + 4x - 7
Calculate the indicated function values in the following problems.
.
.
.
14. f(10)
16. f(a)
18. g(10)
20. g(a)
22. h(10)
24. h(a)
15. f(-2)
17. f(a+b)
19. g(-2)
21. g(a + b)
23. h(-2)
25. h(a+b)
Answer:
Step-by-step explanation:
f(x) = x
g(x) = 5x - 12
h(x) = x² + 4x - 7
===============
14. f(10) = 10
16. f(a) = a
18. g(10) = 38
20. g(a) = 5a - 12
22. h(10) = 133
24. h(a) = a^2 + 4a - 7
15. f(-2) = -2
17. f(a+b) = a + b
19. g(-2) = -12
Suppose E⃗ =2A⃗ +E→=2A→+ 3B⃗ 3B→ where vector A⃗ A→ has components AxAx = 5, AyAy = 2 and vector B⃗ B→ has components BxBx = -3, ByBy = -5.
Therefore, the components of vector E⃗ are Ex = 1 and Ey = -11. Thus, E⃗ = (1, -11).
To solve this equation, let's break it down component-wise. Given:
E⃗ = 2A⃗ + 3B⃗
We can write the equation in terms of its components:
Ex = 2Ax + 3Bx
Ey = 2Ay + 3By
We are also given the components of vectors A⃗ and B⃗:
Ax = 5
Ay = 2
Bx = -3
By = -5
Substituting these values into the equation, we have:
Ex = 2(5) + 3(-3)
Ey = 2(2) + 3(-5)
Simplifying:
Ex = 10 - 9
Ey = 4 - 15
Ex = 1
Ey = -11
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Is (1,1) a unit vector? Explain. Choose the correct answer below.A. (1,1) is not a unit vector, since the sum of its components is not 1. B. (1,1) is a unit vector, since its length is 1. C. (1,1) is a unit vector, since each of its components has a magnitude of 1. D. (1,1) is not a unit vector, since its length is not 1.
The each component of (1,1) also has a magnitude of 1/sqrt(2), but this is not necessary for a vector to be a unit vector.
B. (1,1) is a unit vector, since its length is 1.
A unit vector is a vector with a magnitude of 1. The magnitude of a vector (a,b) is given by the formula ||(a,b)|| = sqrt(a^2 + b^2).
For the vector (1,1), the magnitude is ||(1,1)|| = sqrt(1^2 + 1^2) = sqrt(2), which is not equal to 1. However, to be a unit vector, it is only necessary for the magnitude to be 1, so (1,1) is indeed a unit vector.
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Griffiths Fig. 5.48 is a handy "triangle" summarizing the mathematical connections between and But there's a missing link; he has nothing for the left arrow from to Note the equations defining are very analogous to the basic Maxwell's equations for B: So depends on in the same way (mathematically) that depends on (Think Biot-Savart!) Use this idea to just write down a formula for in terms of B to finish off that triangle. In Griffiths Ex. 5.9 he found the B field everywhere inside (and outside) an infinite solenoid (which you can think of as a cylinder with uniform surface current flowing azimuthally around it. See Griffiths. Fig 5.35. Use the basic idea from part 1a to, therefore, quickly and easily just write down the vector potential in a situation where looks analogous to that, i.e. with C constant. Sketch What physical situation creates such a B field?
Formula for A in terms of B: A = ∫(B × r') / ||r - r'|| dr'
The missing link in the triangle summarizing the mathematical connections between A and B can be filled by writing down a formula for A in terms of B. This can be done by using the analogy between the equations defining A and the basic Maxwell's equations for B, and applying the Biot-Savart law. By using the basic idea from the first part, the vector potential in a situation where B is constant can be quickly found.
Physical situation creating constant B field:
A constant B field can be created by a current-carrying wire in the form of a straight line or a circular loop. The vector potential for this configuration can be found using the formula derived above.
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Zarin drinks 16 glasses of water in one day. If she drinks same amount of water
every day, then how much water does she drink in one week?
Answer:
the answer is 112 glasses of water.
Step-by-step explanation:
let's use a proportion method
16glasses=1 day
and the whole week is composed of 7 days this means that:
7 days= 16*7=112 glasses of water
Answer:
112
Step-by-step explanation:
because 16 * one week ( 7 ) = 112
16 x 7 = 112 ..
I need help with this question
The correct equation for finding the value of d and the the distance between the sun and star is,
⇒ d = x cosФ
Given that;
Diagram for finding the distance between the sun and star.
Let us assume that, the distance between the sun and star is x
Now, We can formulate;
⇒ cos Ф = d / x
⇒ d = x cosФ
Therefore, The correct equation for finding the value of d and the the distance between the sun and star is,
⇒ d = x cosФ
Thus, Correct equation is,
⇒ d = x cosФ
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What is the median of this data set? {13, 13, 13, 15, 15, 16, 16, 17, 177
I NEED HELP ASAP PLEASE
Answer:15
Step-by-step explanation:
its the middle number
Answer: i think it's 15!!
hope this helps lol
Identify the lateral area and the surface area of a right rectangular prism with a 12cm by 10cm base and height 16cm.
Answer:
944 cm²
Step-by-step explanation:
get the area of each side: 12*10+10*16+12*16= 472
2 sets of each side: 944
Factor completly 4x^2 +8x -5
∑ Hey, jillianwagler ⊃
Answer:
\(\left(2x-1\right)\left(2x+5\right)\)
Step-by-step explanation:
║Given info║:
Factor completely: \(4x^2 +8x -5\)
Solution~:
Breaking the expression~: \(\left(4x^2-2x\right)+\left(10x-5\right)\)
Factor out 2x from 4x² -2x : 2x(2x-1)
Factor out 5 from 10x - 5 : 5(2x - 1)
Put together: \(=2x\left(2x-1\right)+5\left(2x-1\right)\)
Factor out 2x - 1: \(=\left(2x-1\right)\left(2x+5\right)\)
xcookiex12
8/19/2022
solve the following system of equations. if there is no solution, write dne in each coordinate of the ordered triplet. if there are an infinite number of solution, write each coordinate in terms of z . z. x 7
DNE in each coordinate of the ordered triplet are y is -7 , DNE ,y is-2.
Whais the explanation?1.) 2+3 = y + 12
Make y the formula's subject after adding the LHS.
5 = y + 12
Y = 5 - 12
Y = - 7
The answer to the equation is -7
2.) 2 + 13 = 1 +8
The equation cannot have a solution since there is no unknown variable and the sum of the numbers on the left hand side (LHS) does not equal the sum of the numbers on the right hand side (RHS).
3.) y - 7 = 2 - 11
RHS is added, and y is become the formula's subject.
Y - 7 = -9
Y = -9 + 7
Y = -2
The equation's answer is -2.
The complete question is:Solve the following system of equations. If there is no solution, write DNE in each coordinate of theordered triplet. If there are an infinite number of solution, write each coordinate in terms of z.2+3 = y + 12
2 + 13 = 1 +8
y - 7 = 2 - 11
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What are the solutions to the quadratic equation (2b+3)^2=12
Answer:
b=− 3/4 =−1.333
b= 2/3=1.500
explanation
middle term, which is -1 .
-72 + 1 = -71
-36 + 2 = -34
-24 + 3 = -21
-18 + 4 = -14
-12 + 6 = -6
-9 + 8 = -1 That's it
Two real solutions:
b =(1+√289)/12=(1+17)/12= 1.500
or:
b =(1-√289)/12=(1-17)/12= -1.333
Determine whether an observational study or an experimental study is used. Two groups of grocery shoppers were randomly selected. The individuals in Group shopped at a health food supermarket. Group individuals shopped at a neighborhood grocery store. At the end of one month, the average food costs of the two groups were compared.
Since the researcher is merely observing and comparing existing groups without any manipulation or intervention, this study is classified as an observational study.
In an observational study, the researcher observes and collects data on existing groups or individuals without intervening or manipulating any variables. In this case, the researcher selected two groups of grocery shoppers (one group shopping at a health food supermarket and the other at a neighborhood grocery store) and observed their food costs over a month. The researcher did not control or manipulate any factors or assign participants to specific groups.
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Consider two independent binomial experiments. In the first one, 94 trials had 54 successes.In the second one, 63 trials had 40 successes. Answer the following questions. Use a confidence level of 96%. Use 4 decimal places for each answer. Do not round from one part to the next when performing the calculations, though. Find the point estimate. Find the critical value. Find the margin of error. Find the confidence interval. < p 1 − p 2
The 96% confidence interval for the difference in proportions is (−0.1127, 0.3191)
To compare the proportions of success in two binomial experiments, we can use the two-sample Z-test.
Let p1 be the proportion of success in the first experiment and p2 be the proportion of success in the second experiment. We want to test the null hypothesis H0: p1 = p2 against the alternative hypothesis Ha: p1 ≠ p2.
First, we calculate the point estimate of the difference in proportions:
\(pp1 - p2 = \frac{54}{94} - \frac{40}{63} = 0.1032\)
Next, we find the critical value of the test statistic. Since the confidence level is 96%, we have alpha = 0.04/2 = 0.02 on each tail of the distribution. Using a standard normal distribution table, we find that the critical values are ±2.0537.
The margin of error is given by:
\(ME= z \sqrt{\frac{p1(1-p1)}{n1} +\frac{p2(1-p2)}{n2} }\)
where z* is the critical value, n1 and n2 are the sample sizes of the two experiments. Plugging in the values, we get:
\(ME= z \sqrt{\frac{0.5769(1-0.5769)}{94} +\frac{0.6349(1-0.6349)}{63} }= 0.2159\)
Finally, we can construct the confidence interval for the difference in proportions as:
(p1 - p2) ± ME
which gives us:
0.1032 ± 0.2159
Thus, the 96% confidence interval for the difference in proportions is (−0.1127, 0.3191).
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Triangle BCD was dilated using the rule D Subscript Q, one-half.
What are the values of the unknown measures?
m∠C'B'D' =
°
CQ =
B'D' =
The values of the missing angles and sides after dilation are:
m∠C'B'D' = 95°, CQ = 6 and B'D' = 11.
What are the values of the angles after transformation?m∠C'B'D = 180° - m∠B'C'D' - m∠B'D'C'
m∠B'C'D = m∠BCD, m∠B'D'C' = m∠BDC (dilation)
m∠C'B'D = 180° - 34° - 51° = 95°
Thus, by way of scale factor we can say that:
BC/B'C' = BD/B'D' = 36/18 = 2
B'D' = ¹/₂BD = ¹/₂ * 22 = 11
ΔC'P'Q ∼ ΔCPQ
Thus:
C'Q'/CQ = C'D'/CD = D'Q'/DQ
CQ = 2C'Q' = 2 * 3 = 6
Therefore, m∠C'B'D' = 95°, CQ = 6 and B'D' = 11.
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a continuous random variable x has a normal distribution with a mean of 12.25. the probability that x takes a value less than 13 is 0.82. Use this information and the symmetry of the density function to find the probability that X
takes a value greater than 11.50
Sketch the density curve with relevant regions shaded to illustrate the computation.
Given that a continuous random variable x has a normal distribution with a mean of 12.25 and the probability that x is less than 13 is 0.82, we can use the symmetry of the density function to find the probability that x is greater than 11.50.
Since the normal distribution is symmetric, the probability of x being less than 13 is equivalent to the probability of x being greater than the mean minus 13. Therefore, P(x < 13) = P(x > 12.25 - 13).
To find the probability that x is greater than 11.50, we can use the same reasoning. We know that the probability of x being less than 11.50 is equivalent to the probability of x being greater than the mean minus 11.50. Therefore, P(x < 11.50) = P(x > 12.25 - 11.50).
To illustrate the computation, we can sketch the density curve of the normal distribution with the relevant regions shaded. The mean, 12.25, is the center of the distribution. We shade the region to the left of 13, representing P(x < 13), and shade the region to the right of 11.50, representing P(x > 11.50). By using the symmetry of the density function, we can see that the shaded region to the right of 11.50 is equal to the shaded region to the left of 13.
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solve (-2x) x 8x
its a simple question no equations just solve it its a quadratic expression
Answer:
-16x²
Step-by-step explanation:
-2x*8x= -16x²
Simplify 4a^3 b^2 x 6a^6b^9
Answer:
24a^9 b^11
Step-by-step explanation:
\(4a ^{3} b ^{2} \times 6a ^{6} b ^{9} \\ = (4 \times 6)a ^{3 + 6}b ^{2 + 9} \\ = 24a^{9} b^{11} \)
a coin is weighted so that the probability of getting heads is two-thirds. suppose you toss this coin 15 times. let x represent the number of heads. what are the mean and standard deviation of x?
When a coin is weighted, there is a two-thirds chance that it will land on its head. suppose you toss this coin 15 times. let x represent the number of heads. Mean = 10 and Standard deviation = 2.88
The mean of x, which represents the number of heads when the coin is tossed 15 times, is 10. This is because the probability of getting heads is two-thirds, meaning that two out of every three tosses will result in heads.We apply the following formula to determine the standard deviation:
Standard Deviation = √(p*q*n), where p is the probability of getting heads, q is the probability of getting tails, and n is the number of tosses. In this case, p = 2/3, q = 1/3, and n = 15, so the standard deviation of x is 2.88.
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Consider the equation and the graph
Answer:
-33/16
I'm pretty sure it is c sorry if not may be -39/16
write the time that is thirty minutes before midnight. PLEASE HELP ME!!!
Iam wasting my last points on this, so be QUIÇK!!!! THX!!!!!!!!!!!!!!
Answer:
it is 11:30pm
In an international food festival, Milan can try foods from
Korea,Japan,andPeru
. He can choose to try foods from some, none, or all of these countries. In the braces below, list all the possible sets of countries whose food Milan can try.
The possible sets of countries whose food Milan can try are as follows:
1. {Korea}
2. {Japan}
3. {Peru}
4. {Korea, Japan}
5. {Korea, Peru}
6. {Japan, Peru}
7. {Korea, Japan, Peru}
These sets represent all the possible combinations of trying foods from Korea, Japan, and Peru, including trying food from one country, two countries, or all three countries.
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4. A punch bowl holds 80 oz of punch, that is enough for exactly 16 servings.
Hillary says that there are 20oz of punch for every 5 servings. Is Hillary correct?
Answer:
No, Hillary is incorrect. There's 20oz of punch for every 4 servings.
Step-by-step explanation:
80oz / 20oz = 4
16 servings / 4 = 4 servings
So, instead of there being 20oz of punch for every 5 servings, there would be 20oz of punch for every 4 servings.
11. Engineering The maximum load for a certain elevator is 2000 pounds. The total
weight of the passengers on the elevator is 1400 pounds. A delivery man who weighs
243 pounds enters the elevator with a crate of weight w. Write, solve, and graph an
inequality to show the values of w that will not exceed the weight limit of the elevator.
The inequality to show the values of [w] that will not exceed the weight limit of the elevator is w + 1643 ≤ 2000. On solving the inequality, we get w ≤ 357. The graph of the inequality is attached.
What is inequality?In mathematics, an inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions. It is used most often to compare two numbers on the number line by their size.An inequality is a mathematical relationship between two expressions and is represented using one of the following -≤ : less than or equal to
≥ : greater than or equal to
< : less than
> : greater than
≠ : not equal to
Given is the maximum load for a certain elevator is 2000 pounds. The total weight of the passengers on the elevator is 1400 pounds. A delivery man who weighs 243 pounds enters the elevator with a crate of weight [w].
We can write the inequality as follows -1400 + 243 + w ≤ 2000
w + 1643 ≤ 2000
Solving the inequality, we get -w + 1643 ≤ 2000
w ≤ 2000 - 1643
w ≤ 357
Refer to the graph attached.Therefore, the inequality to show the values of [w] that will not exceed the weight limit of the elevator is w + 1643 ≤ 2000. On solving the inequality, we get w ≤ 357. The graph of the inequality is attached.
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Mason is planning to buy a car two years from now. He currently has $400 saved up to buy the car. From all the cars Mason is considering buying, how much money to save per month over the next two years if the least expensive car he wants to buy is $4000
Answer:150 dollars
Step-by-step explanation:
3600 (cost of car) divided by 24 (months)
The probability that two cards are selected at random from a deck of cards containing
a face card and diamond without replacement.
Simplify-80)
(-20)
04
04
0-40
40
Help please
Answer:
the second choice which is positive 4 is the answer
Answer:
4
Step-by-step explanation:
(-80)/(-20)=
(-40)/(-10) when divided by 2
(-20)/(-5) when divided by 2 again
(-4)/(-1) when divided by 5
4 when divided by -1
Hope this helps
(pls mark brainliest)
Ok so I got the answer x=6.9 and its rounded to the nearest tenth
Answer:
Using the Similar Right Triangle theorem:
\(\mathsf{\dfrac{segment \ 1}{altitude}=\dfrac{altitude}{segment \ 2}}\)
Given:
segment 1 = 6segment 2 = 8altitude = \(x\)\(\implies \dfrac{6}{x}=\dfrac{x}{8}\)
\(\implies 48=x^2\)
\(\implies x=\sqrt{48}\)
\(\implies x=\sqrt{16 \cdot 3}\)
\(\implies x=\sqrt{16} \sqrt{3}\)
\(\implies x=4\sqrt{3}\)
\(\implies x=6.9 \textsf{ (nearest tenth)}\)
A 12 inch line segment is divided into two parts. Which
of the following lengths result in a ratio closest to the
golden ratio, ?
2
1+v5
O A. 6 inches and 6 inches
O B. 7 inches and 5 inches
C. 7.5 inches and 4.5 inches
O D. 7.75 inches and 4.25 inches
The length which result in a ratio closest to the golden ratio is equal to 7.5 inches and 4.5 inches. Option C is correct.
What is the length of line segment?The line segment is made with two end points. Length of a line segment is the distance of both the ends of it.
A 12 inch line segment is divided into two parts. Suppose the line segment is AC which is divided into AB and BC parts. Thus,
AB+BC=AC
AB+BC=12 ....1
The value of golden ratio is equal to 1.618. It can also be given as (1+√5)/2. The ratio of both segment is equal to golden ratio. Thus
\(\dfrac{AB}{BC}=\dfrac{AC}{AB}=\dfrac{1+\sqrt{5}}{2}\\\dfrac{12}{AB}=1.618\\AB=7.4166 \rm\; in\)
Put this value in equation one as,
AB+7.4166=12
AB=4.5834
The length which result in a ratio closest to the golden ratio is equal to 7.5 inches and 4.5 inches. Option C is correct.
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Select all of the expressions that are equivalent to 5% of 60. 1/20(60), 1/5 times 60, 0.05 times 60, 0.5 times 60, 0.5(60), 5/100 times 60
The expressions that are equivalent to 5% of 60 are 5/100 * 60, 0.05 * 60 and 1/20 * 60
How to determine the expressions that are equivalent to 5% of 60?The expression is given as:
5% of 60
Express as fraction and decimal
5% of 60 = 5/100 * 60
5% of 60 = 0.05 * 60
This gives
5% of 60 = 1/20 * 60
Hence, the expressions that are equivalent to 5% of 60 are 5/100 * 60, 0.05 * 60 and 1/20 * 60
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A sailboat costs $22,205. You pay 25% down and amortize the rest with equal monthly payments over a 13-year period. If you must pay 8.1% compounded monthly, what is your monthly payment? How much interest will you payMorthly payments: $(Round to two decimal places)
The amortization formula is given by
\(PV=PMT\times(\frac{1-(1+\frac{r}{n})^{-nt}}{\frac{r}{n}})\)Where
\(\begin{gathered} PV\rightarrow Present\text{ value} \\ \text{PMT}=\text{Monthly payment} \\ r=\text{anual rate} \\ n=\text{number of compounding} \\ t=\text{ time in years} \end{gathered}\)Since there is 25% down payment, then PV will be
\(22,205-(25\%\times22,205)\)\(\begin{gathered} PV=22,205-(\frac{25}{100}\times22,205) \\ =22205-5551.25 \\ =16653.75 \end{gathered}\)Given the following
\(\begin{gathered} r=\frac{8.1}{100}=0.081 \\ \frac{r}{n}=\frac{0.081}{12}=0.00675 \\ t=13 \\ nt=12\times13=156 \end{gathered}\)Substitute the values above in the amortization formula
\(\begin{gathered} PV=PMT\times(\frac{1-(1+\frac{r}{n})^{-nt}}{\frac{r}{n}}) \\ 16653.75=\text{PMT}\times(\frac{1-(1+0.00675)^{-156}}{0.00675}) \end{gathered}\)\(\begin{gathered} 16653.75=\text{PMT}\times\frac{1-1.00675^{-156}}{0.00675} \\ 16653.75=\text{PMT}\times\frac{1-0.3501260533}{0.00675} \\ 16653.75=\text{PMT}\times\frac{0.6498739467}{0.00675} \\ 16653.75=\text{PMT}\times96.27762173 \end{gathered}\)\(\text{PMT}=\frac{16653.75}{96.27762173}=172.9763335\)Hence, the monthly payment is approximately $172.98